Effects of Selective Attention on Mean-Size Computation: Weighted Averaging and Perceptual Enlargement

Abstract

For efficient use of limited capacity, the visual system summarizes redundant information and prioritizes relevant information, strategies known respectively as ensemble perception and selective attention. Although previous studies showed a close relationship between these strategies, the specific mechanisms underlying the relationship have not been determined. We investigated how attention modulated mean-size computation. Fourteen people participated in this study. We hypothesized that attention biases mean-size computation by increasing the contribution (weighted averaging) and the apparent size (perceptual enlargement) of an attended item. Consistent with this hypothesis, our results showed that estimated mean sizes were biased toward the attended size and overestimated regardless of the attended size, supporting weighted averaging and perceptual enlargement, respectively. Taken together, the observed effects of selective attention on mean-size computation signify a close relationship between the two optimization mechanisms to achieve efficient management of the visual system’s limited capacity.

Keywords

ensemble perception mean size selective attention weighted averaging perceptual enlargement open data open materials

Our visual system continuously encounters complex and cluttered information distributed across a scene but has limited resources to process it (Palmer, 1990). To overcome these limitations and optimize information processing, our visual system applies two complementary strategies: ensemble perception and selective attention.

First, we summarize complex and redundant information into statistical summaries (Alvarez, 2011). This ability to form statistical representation includes not only low-level visual features such as orientation (Parkes, Lund, Angelucci, Solomon, & Morgan, 2001) and size (Chong & Treisman, 2003) but also high-level features such as emotion (Haberman & Whitney, 2007) and biological motion (Sweeny, Haroz, & Whitney, 2013). In the present study, we focused on the ability to compute the mean sizes of stimuli to understand the effect of attention on ensemble perception. The second way to overcome limited capacity is to prioritize relevant information by attention, which enables efficient allocation of limited resources (Carrasco, 2011). Observers have shown faster and more accurate responses when the location of the target was attended either before or after the presentation of stimuli (Souza & Oberauer, 2016).

To optimize information processing, ensemble representation and attention should work together even though they cope with limited capacity differently. Previous studies have suggested a close relationship between ensemble perception and attention (Chong & Treisman, 2005; De Fockert & Marchant, 2008; Im, Park, & Chong, 2015; Li & Yeh, 2017). Attention increased the contribution of an attended size during mean-size computation (De Fockert & Marchant, 2008; Li & Yeh, 2017), and ensemble representation was used as a unit of selection (Im et al., 2015). Although numerous pieces of evidence support a close relationship between attention and mean-size computation, few studies have investigated its underlying mechanisms.

Here, we investigated two effects of attention on mean-size representation—weighted averaging and perceptual enlargement. When multiple sizes are integrated into mean size, the relative contribution of an attended size can be greater than other sizes. The averaging process is influenced by saliency (Kanaya, Hayashi, & Whitney, 2018) and attention (De Fockert & Marchant, 2008). Kanaya and colleagues (2018) found that more salient items make a greater contribution toward averaging than less salient items. De Fockert and Marchant (2008) asked participants to locate the largest or smallest item within a set to manipulate the size of an attended item during a mean-size-discrimination task. They found that participants were more likely to overestimate mean size when the largest item was located, suggesting increased contribution of the attended size. The weighted averaging due to attention is illustrated as a positive slope in Figure 1. As selective attention increases the contribution of an attended size, calculated mean size will be biased toward the attended size. That is, bias in mean-size estimation will increase as a function of the attended size.

Fig. 1.

Schematic illustration of hypothetical effects of selective attention on mean-size estimation. Estimation bias, which refers to the relative difference between the reported and actual mean sizes of an attended item, is shown as a function of the size of the attended item. The solid and dashed lines indicate how mean-size estimation changes depending on selective attention directed either before (precue) or after (postcue) the stimuli presentation. Two effects of selective attention are illustrated: weighted averaging and perceptual enlargement. In weighted averaging, selective attention increases the contribution of an attended size, which in turn biases calculated mean size toward the attended size. In perceptual enlargement, an individual stimulus appears larger because of attention, which results in the apparent mean size of a set increasing.

Selective attention toward an individual item can increase the apparent size of the attended item, resulting in overestimated mean size. Attention can change the appearance of attended stimuli (for a review, see Carrasco and Barbot, 2019). For example, Kirsch, Heitling, and Kunde (2018) found an increased size of a circle from both exogenous and endogenous attention. Furthermore, perceived size, not retinal size, has been used for mean-size computation (Im & Chong, 2009). Therefore, when the individual stimulus appears larger because of attention, the apparent mean size of a set will increase as well. Such overestimation is illustrated as an increased intercept in Figure 1.

To test weighted averaging and perceptual enlargement, we designed an experiment with two major modifications that resolved limitations of previous studies (De Fockert & Marchant, 2008; Kanaya et al., 2018; Li & Yeh, 2017). First, we manipulated the temporal location of attention to be either before (precue) or after (postcue) the presentation of stimuli. Because attention changes appearance only when it is directed before the stimulus presentation (Carrasco & Barbot, 2019), this manipulation allowed us to dissociate the effect of weighted averaging from that of perceptual enlargement. If a postcue does not alter apparent size, the postcue condition will show only an increased slope because of weighted averaging (Fig. 1). On the contrary, a precue will increase both the slope and the intercept because of both weighted averaging and perceptual enlargement. To quantitatively measure and test these predictions, we used an adjustment method in which participants estimated the mean size of a test set by adjusting that of a probe set.

Second, we varied the size of attended items. Previous studies tested only a limited number of attended sizes (De Fockert & Marchant, 2008; Li & Yeh, 2017). Although such manipulations sufficed to confirm the effect of attention on mean-size computation, they were not enough to compare the relative contributions of different sizes with mean-size computation. Therefore, we directed attention toward not only two extreme sizes but also intermediate sizes in the current study to find systematic changes in estimation errors as a function of attended sizes.

In the present study, we investigated how selective attention to an individual size changed mean-size estimation. After a set of gratings with different sizes and orientations was presented, participants reported both the mean size of a set and the individual orientation of the cued grating. Using this dual-task paradigm, we manipulated the temporal location of attention and the size of an attended item. Our results support the predicted effects of attention, weighted averaging, and perceptual enlargement. Selective attention biased mean-size representation by increasing either the contribution or the apparent size of the attended item.

Method

Participants

Fourteen observers from Yonsei University participated in the experiment. All participants were between 24 and 29 years old (eight female; age: M = 27 years, SD = 1.36) and reported normal or corrected-to-normal vision. They were all naive to the hypothesis. Participants submitted written consent forms before participating, and every process and detail about the experiment was conducted in accordance with the guidelines of the Yonsei University Institutional Review Board.

A recent article suggested a new method whereby a sample size with more precise statistical power can be computed by correcting publication bias and uncertainty (Anderson, Kelley, & Maxwell, 2017). Necessary parameters were obtained from an experiment with a similar design and hypothesis (De Fockert & Marchant, 2008, Experiment 2). The alpha level for the planned study was set to .001 on the basis of both the previous p value and a recently suggested p-value criterion (p < .005) for statistical significance testing (Benjamin et al., 2018). The desired levels of assurance and statistical power were .8. As a result, the Web application (for the two-way within-subjects analysis of variance, or ANOVA) yielded a minimum sample size of nine participants. However, we added five additional participants because of experimental and hypothetical differences between our study and the previous study (De Fockert & Marchant, 2008).

Apparatus

All stimuli were generated using MATLAB (The MathWorks, Natick, MA) with the Psychophysics Toolbox (Version 3 extension; Brainard, 1997; Kleiner, Brainard, & Pelli, 2007; Pelli, 1997). Stimuli were presented on a uniform gray background (31.31 cd/m²) of a 21-in. CRT monitor (HP P1230) with a 1,600 × 1,200 resolution and 85-Hz refresh rate. The participants placed their heads on a forehead and chin rest that was fixed 60 cm from the monitor. One degree of visual angle was subtended by 41.89 pixels.

Stimuli

Participants were asked to report not only the mean size of a set but also the orientation of a single grating. A test set consisted of eight gratings with different sizes and orientations, each located on the vertex of a regular octagon with a radius of 5°. Each sine grating had a spatial frequency of 2.2 cycles per degree with full contrast, demarcated with a circular mask. Throughout the experiment, the mean size and individual size of the eight gratings were computed after converting physical area into perceived area by a power function with an exponent of .76 (Chong & Treisman, 2003; Teghtsoonian, 1965).

Figure 2a shows how each size of the eight gratings in a test display was generated from a selected mean size. At the beginning of every trial, we first randomly selected a mean size for the test set between 1.54 and 4.15 degrees squared, and eight different sizes were then generated with the following constraints. First, the mean of the eight sizes was set to match the selected mean size. Second, the size of gratings was calculated with constant differences between the to-be-attended gratings. Starting from the smallest grating among the set (first), the sizes of the third, sixth, and eighth (largest) gratings increased by 10% (Fig. 2a). The sizes of the other gratings that were not included in the size condition (second, fourth, fifth, and seventh) were interpolated to have an equal distance between adjacent sizes. Notably, a grating of the mean size was never presented as a member of a test set. We also varied the orientation of each grating for the orientation-discrimination task. Each orientation of a grating was randomly selected between 15° and 75° from the vertical in either the clockwise or counterclockwise direction.

Fig. 2.

Method of stimulus generation and example trial sequences. Eight different sizes constituting a single set of gratings were generated from the selected mean size (a). The relative size difference between each attended size (first, third, sixth, eighth) was 10%, and the sizes of the remaining gratings were interpolated for each size condition. The procedure of a single trial is shown for the precue condition (b) and the postcue condition (c). In both conditions, participants were shown a test set of eight stimuli. In the precue condition, participants were asked to remember both the mean size of the test set and the individual orientation of a grating that was cued before the set appeared. In the postcue condition, they were asked to remember the orientation of every individual grating as well as the mean size of the test set, and a cue after the test set disappeared indicated which of the items’ orientations to report. Participants in both conditions reported the mean size of the test set and whether the designated grating was tilted clockwise or counterclockwise.

In the adjustment phase, participants were asked to adjust the overall size of a probe set to match that of a test set. To minimize representational disparity between two grating sets, we generated a probe set to resemble the appearance of the test set. Although the size of each grating was generated with the same method as in a test set, the orientation of gratings in the probe set was kept vertical. The initial mean size of a probe set was randomly selected within a range between the smallest and largest gratings of the presented test set. As participants adjusted the mean size of the probe set, the diameter of its mean size increased or decreased by 1.5 pixels (0.036°). After each adjustment, new gratings were generated using the same procedure and were randomly placed on the vertices of an octagon.

Procedure

A mean-size-estimation task and an orientation-discrimination task were combined within a single trial. The experiment had a 2 (cuing condition) × 4 (size condition) within-subjects design. Cuing condition indicated whether the arrow cue was presented before (precue condition) or after (postcue condition) a test set, and the four size conditions varied according to the size of attended gratings. Each condition was repeated 50 times, producing a total of 400 trials across the whole experiment. The two cuing conditions were tested in a separate session, and their order was counterbalanced across participants. The size conditions were intermixed within a single session. Therefore, participants were assigned 200 trials in a single session with four blocks of 50 trials. Participants took as much time as needed for a break between each block. Additionally, we presented 20 practice trials before each session to ensure that participants were familiar with the procedure. Audio feedback was provided only for the individual orientation task during a practice session. The experiment was performed in a dark room. Participants were asked to keep their eyes on the fixation cross throughout the experiment. As shown in Figure 2, the sequence of displays within a single trial was different depending on the cuing condition.

Figure 2b shows the procedure of a single trial in the precue condition. After a 1,000-ms blank display with a fixation cross, a precue display with an arrow pointing at the location of a to-be-reported grating for the orientation-discrimination task appeared for 200 ms. After a 100-ms blank display, a test set was presented for 500 ms. Participants were asked to remember both the mean size of the test set and the individual orientation of the cued grating. There was then a 500-ms blank display before the orientation-task display. This retention interval was included so the delay before the presentation of the probe set would be the same in both the precue and postcue conditions. After the retention interval, orientation- and mean-size-task displays were presented in order. First, participants reported whether the designated grating was tilted clockwise or counterclockwise using the “right” or “left” arrow keys, respectively. Participants then reported the mean size of the test set by adjusting the mean size of a probe set to match that of the test set using “up” or “down” arrow keys. They moved to the next trial by pressing the space bar after finishing their adjustments.

The procedure of the postcue condition is illustrated in Figure 2c. A blank display with a fixation cross was presented for 1,000 ms at the beginning of each trial, and a test set was subsequently presented for 500 ms. Whereas participants remembered the orientation of a single attended grating and mean size of the set in the precue condition, they were asked in the postcue condition to remember the orientation of every individual grating as well as the mean size of the test set. After the test display, a 100-ms retention period was followed by a postcue display. At that time, participants reported the orientation of the single grating at the cued position. Immediately after the orientation-discrimination task, a probe set for mean-size estimation was presented. In both tasks, the method of responding was identical to that in the precue condition.

Analysis

The main purpose of the present study was to investigate how attention to individual size modulated mean-size computation. We first analyzed performance in the orientation-discrimination task to ensure that attention was properly directed to a targeted grating. Accuracy in the orientation-discrimination task was analyzed with a 2 (cuing condition) × 4 (size condition) repeated measures ANOVA.

Next, we tested whether participants actually reported the mean size of the test set instead of an attended size. Estimated mean sizes were regressed on the actual mean size and the attended size. The multicollinearity assumption of simple multiple regression was violated because of inevitable covariance between the two predictors, so we used hierarchical multiple regression by entering the two predictors into separate models. The estimated R² change in the second model compared with the first model indexed the additional or exclusive predictability of one predictor after the variance of the other was accounted for. Each regression was conducted for each participant after the data were pooled across conditions.

After checking the reliability of our manipulations, we analyzed the results of a mean-size-estimation task. We first calculated the trial-by-trial relative error (%) of estimated mean size using the following equation:

relative error (%) = 100 \times \frac{estimated size - mean size}{mean size} .

Positive and negative relative error indicated the overestimated and underestimated mean sizes, respectively. Afterward, individual error data were fitted to a normal distribution for each condition. The standard deviation (σ) and mean (μ) of the distribution were statistically analyzed across conditions. The standard deviation of the distribution indicated the precision of mean-size estimation and its mean indicated estimation bias.

Throughout the analysis, both frequentist and Bayesian ways of testing statistical significance were applied using MATLAB (MathWorks, Natick, MA) and JASP (Version 0.10.0.0; JASP Team, 2017; Wagenmakers et al., 2018).

Results

Attentional modulation: orientation-discrimination task

We first checked whether selective attention was directed toward individual size as intended. We performed separate one-sample t tests for each condition within a 2 (cuing condition) × 4 (size condition) design. In every condition, accuracy was significantly higher than chance (> 50%; ps < .001), as shown in Figure 3a, indicating successful modulation of attention.

Fig. 3.

Orientation-task performance (a) and results from the hierarchical multiple regression (b). For the orientation task, accuracy in each cuing condition is shown separately for each size condition. Chance was 50% correct. For the multiple-regression results, the R² change between the two models is shown for each predictor. The different symbols indicate different participants. In both graphs, error bars indicate 95% confidence intervals.

Although participants reliably attended a targeted item, the amount of attention given to the item might vary across conditions. For instance, larger stimuli could have captured more attention and been prioritized (Im et al., 2015; Kanaya et al., 2018; Proulx, 2010). If larger stimuli capture more attention, the accuracy should be higher for larger sizes. To test whether such prioritization took place in our experiment, we performed a 2 × 4 repeated measures ANOVA.

As shown in Figure 3a, participants performed comparably across size conditions, F(3, 39) = 1.43, p = .248, η_p² = .10, Bayes factor favoring the alternative over the null hypothesis (BF₁₀) = 0.05. However, orientation-task performance was significantly higher in the precue condition than the postcue condition, F(1, 13) = 43.77, p < .001, η_p² = .77, BF₁₀ = 3.980 × 10²⁶, because participants had to remember more orientations in the postcue condition. There was no significant interaction between the size condition and the cuing condition, F(3, 39) = 0.30, p = .823, η_p² = .02.

Mean size versus attended size: hierarchical multiple regression

Although participants were asked to report the mean size of the gratings, it is possible that they sampled a limited number of items (e.g., Myczek & Simons, 2008). In particular, because a single grating was attended in every trial, it is plausible that participants reported only the size of the cued grating. To rule out this possibility, we regressed estimated mean sizes on the actual mean and attended sizes.

Figure 3b compares the R² change between the first and second models to show how much one predictor explains the data over the other. We found that the mean size showed more additional predictability than the attended size for every participant. At the group level, a paired-samples t test revealed significant differences between the two predictors’ R² change. The R² change for the mean size (M = .084, SD = .036, 95% confidence interval, or CI = [.06, .10]) was significantly larger than that for the attended size (M = .010, SD = .008, 95% CI = [.01, .02]), t(13) = −6.62, p < .001, d = −1.77, BF₁₀ = 1,396. These results suggest that the actual mean size of a set predicted participants’ mean-size estimation even after analyses accounted for the alternative strategy of using the attended size. Thus, it is reasonable to assume that participants averaged sizes, as they had been asked to do.

Mean-size estimation

We varied the temporal location and size of an attended item to investigate how selective attention modulated mean-size computation. First and foremost, we found evidence supporting the two effects of selective attention: weighted averaging and perceptual enlargement (Fig. 4a). According to our hypothesis of weighted averaging, estimated mean size should be biased toward attended size, and this trend would be summarized as a positive slope with increasing bias as a function of the attended size. In addition, mean size should be overestimated regardless of the attended size because of perceptual enlargement. As shown in Figure 4a, the effect of weighted averaging, indicated by positively sloped lines, was found for both the precue and postcue conditions. Furthermore, mean size was overestimated more in the precue condition than in the postcue condition because of perceptual enlargement.

Fig. 4.

Results for estimation bias. Mean estimation bias (a) and standard deviation in estimation bias (b) are each shown as a function of size condition and cuing condition. Relative estimation error was fitted to the normal distribution for each condition. Standard deviation (σ) and mean (μ) from the fitted normal distribution were analyzed. Error bars indicate 95% confidence intervals.

These findings were supported by a 2 × 4 repeated measures ANOVA. Whereas the main effect of cuing condition was not significant, F(1, 13) = 2.01, p = .180, η_p² = .13, BF₁₀ = 3.89, there was a significant main effect of size condition, F(3, 39) = 44.85, p < .001, η_p² = .79, BF₁₀ = 11,002.05. Importantly, we found a significant interaction between the two conditions, F(3, 39) = 11.61, p < .001, η_p² = .47, BF₁₀ = 5.69. According to the Bayes factor, the model with both main effects and the interaction effect (BF₁₀ = 655,073.83) was about 6 times more likely than the model with only two main effects (BF₁₀ = 109,974.83).

To investigate the nature of the interaction between the two factors, we separately analyzed the precue and postcue conditions. The precue condition, indicated by a solid line in Figure 4a, clearly showed increasing estimation bias as a function of the attended size, F(3, 39) = 49.70, p < .001, η_p² = .79, BF₁₀ = 1.473 × 10¹⁰. Bonferroni post hoc comparisons revealed significant differences between every pair of size conditions (ps < .018). Thus, the effect of weighted averaging was manifested at every attended size.

However, the postcue condition showed a less-apparent effect of weighted averaging (Fig. 4a). Significant effects of the attended size were found in the postcue condition, F(3, 39) = 8.32, p < .001, η_p² = .39, BF₁₀ = 114.33. Unlike in the precue condition, however, only the estimation bias of Size Condition 4 (M = 7.28, SD = 10.16, 95% CI = [1.41, 13.14]) was significantly larger than that of the other size conditions in the postcue condition (ps < .006). The contribution of individual size during mean-size computation was increased only when the largest grating was attended.

As perceptual enlargement predicts, mean size was mostly overestimated in the precue condition compared with the postcue condition (Fig. 4a). We ran one-sample t tests for each condition. When attention was directed before the presentation of stimuli, estimation bias was significantly above zero for Size Condition 2 (M = 5.75, SD = 8.41, 95% CI = [0.89, 10.60]), t(13) = 2.56, p = .024, d = 0.68, BF₁₀ = 2.81; Size Condition 3 (M = 8.58, SD = 8.15, 95% CI = [3.88, 13.29]), t(13) = 3.94, p = .002, d = 1.05, BF₁₀ = 24.95; and Size Condition 4 (M = 10.94, SD = 8.41, 95% CI = [6.08, 15.80]), t(13) = 4.87, p < .001, d = 1.30, BF₁₀ = 108.00. On the other hand, when attention was directed after the presentation of stimuli, mean size was significantly overestimated only for Size Condition 4 (M = 7.28, SD = 10.16, 95% CI = [1.41, 13.14]), t(13) = 2.68, p = .019, d = 0.72, BF₁₀ = 3.88.

Next, the precision of mean-size estimation was not modulated by attention. A repeated measures ANOVA showed that standard deviation did not differ by either cuing condition or size condition (Fig. 4b). Because Mauchly’s test indicated the violation of the sphericity assumption for the size condition, χ²(5) = 22.56, p < .001, we used Greenhouse-Geisser correction to report degrees of freedom. The result showed no significant effect of size condition, F(1.43, 18.6) = 2.70, p = .106, η_p² = .17, BF₁₀ = 0.13, or cuing condition, F(1, 13) = 2.69, p = .125, η_p² = .17, BF₁₀ = 64.12. Notably, the main effect of cuing condition showed a seemingly paradoxical mismatch between p value and BF₁₀. Whereas the p value for the cuing condition was not significant (p = .125), BF₁₀ supported a very strong effect of cuing condition (BF₁₀ = 64.121; Jeffreys, 1961). We further analyzed the result using a Bayesian repeated measures ANOVA, including not only fixed effects but also random effects to resolve this discrepancy. Judging from the additional analysis, the abnormally high Bayes factor for the cuing effect might have been partially driven by the random effect of participants (inclusion Bayes factor = 2.470 × 10¹³). Thus, we cannot conclude that the temporal location of cuing changed the precision of mean-size estimation. Note that every condition in our study involved selective attention. Thus, there was no reason to expect precision differences across size conditions.

Discussion

In the present study, we investigated how selective attention toward individual size modulated mean-size computation. To test this, we combined a mean-size-estimation task and an individual orientation-discrimination task within a single trial. By varying the temporal location of an attentional cue and the size of an attended item, we demonstrated the two effects of selective attention: weighted averaging and perceptual enlargement. We found that estimated mean size was biased toward an attended size because of its increased contribution. Additionally, mean size was overestimated mostly when attention was directed before the presentation of stimuli because of increased apparent size.

Weighted averaging

We found evidence supporting weighted averaging as a result of selective attention toward individual size, consistent with previous studies (De Fockert & Marchant, 2008; Kanaya et al., 2018; Li & Yeh, 2017). We varied the temporal location of attention and found the effects of attention not only before but also after the presentation of stimuli, unlike previous studies. Attention to an item is thought to increase its precision by reducing internal noise (Lu & Dosher, 1998), and the reduced noise increases the precision of averaging (Baek & Chong, 2020). Thus, mean representation will become more precise and be biased toward an attended size if the visual system gives more weight to an attended item during averaging on the basis of its relative precision. Nevertheless, the weights of each item during averaging could not be calculated in the current study, unlike in previous studies (Hubert-Wallander & Boynton, 2015; Rodriguez-Cintron, Wright, Chubb, & Sperling, 2019), because of multicollinearity between individual sizes within a test set. Future studies need to investigate how individual contributions are related to their precision.

Weighted averaging found in the postcue condition suggests that ensemble representation should be dynamic and malleable because attention was directed after the stimuli. Hubert-Wallander and Boynton (2015) found that people can average the size of sequentially presented items, suggesting that ensemble representation is flexible enough to update subsequent information. Despite dissimilar experimental designs, the previous study and our results provide converging evidence supporting dynamic ensemble representation.

Another implication of weighted averaging in the postcue condition suggests that participants maintained not only the mean size but also most individual sizes. People are known to hierarchically represent both summary and individual information when processing multiple items (Brady & Alvarez, 2011; Son, Oh, Kang, & Chong, 2020). For example, Brady and Alvarez (2011) found that the size of an individual circle was biased toward the mean size of the same color group. Similarly, we found that the size of a postcued item modulated ensemble representation. Thus, representations of ensemble and individual information are hierarchically organized and interact with each other.

Finally, our results suggest that mean size is calculated by averaging most items rather than sampling a few (e.g., Myczek & Simons, 2008). Because participants had no idea which grating would be attended during the presentation of a set in the postcue condition, significant weighted averaging suggests that most items contributed to averaging, consistent with the findings of previous studies (Baek & Chong, 2020; Chong, Joo, Emmanouil, & Treisman, 2008). The results of our hierarchical multiple regression also support this conclusion.

Weighted averaging was less evident in the postcue condition. One possibility is that larger items, or at least a limited number of items, could have remained intact at the time of a postcue presentation because salient information decays at a slower rate (Proulx, 2010). This is consistent with the significant estimation bias found only in the largest size condition. Another possible explanation is high attentional loads involved with the orientation-discrimination task. In a previous study, a secondary task with high attentional loads deteriorated the representation of individual items, indicated by decreased postcue benefit (Persuh, Genzer, & Melara, 2012). Because observers had to remember all the presented orientations, orientation-task performance was lower in the postcue condition, indicating higher memory loads. Finally, participants could have attended to incorrect gratings considering imperfect performance in the orientation-discrimination task. This would reduce the degree of weighted averaging.

Perceptual enlargement

In addition to weighted averaging, we showed perceptual enlargement as an effect of selective attention. Specifically, we found overestimated mean sizes for three attended sizes of the precue condition but only for the largest size of the postcue condition. This indicates that selective attention makes people overestimate mean size by increasing the apparent size of the attended item, consistent with the findings of previous studies (De Fockert & Marchant, 2008; Li & Yeh, 2017). However, when attention was not directed to one of the items included in averaging, previous studies found no mean-size overestimation (Allik, Toom, Raidvee, Averin, & Kreegipuu, 2013; Baek & Chong, 2020; Lee, Baek, & Chong, 2016). Thus, mean-size overestimation is likely due to perceptual enlargements of individual sizes by attention, especially before the presentation of stimuli (Gobell & Carrasco, 2005).

Apparent size may increase because receptive fields are shifted toward the locus of attention (Anton-Erxleben & Carrasco, 2013; Kirsch et al., 2018). Anton-Erxleben and Carrasco (2013) proposed that size attended to appears larger because the item attended to activates more neurons as a result of the receptive field shift. We think that the increased size of an attended item produced overestimated mean sizes in our study, consistent with this suggestion.

Conclusions

To make the best use of our limited cognitive resources, the visual system applies two complementary strategies: ensemble perception and selective attention. Whereas the former summarizes as much information as possible, the latter prioritizes relevant information. Nevertheless, ensemble representation should not be too rigid to consider all items equally regardless of their importance. Similarly, prioritization should also consider overall information across dimensions of selection. Indeed, previous studies have shown that average orientation was calculated with the consideration of a given context (Cha & Chong, 2018) and that selection was based on statistical summaries (Im et al., 2015). Likewise, we found that ensemble representation was formed with the consideration of selective attention. Attention biased mean-size estimation by increasing both the contribution and the apparent size of an attended item. Taken together, the present study extends our understanding of how the complementary relationship between ensemble perception and attention achieves the goal of using our limited capacity efficiently.

Supplemental Material

Chong__OpenPracticesDisclosure_rev – Supplemental material for Effects of Selective Attention on Mean-Size Computation: Weighted Averaging and Perceptual Enlargement

Supplemental material, Chong__OpenPracticesDisclosure_rev for Effects of Selective Attention on Mean-Size Computation: Weighted Averaging and Perceptual Enlargement by Yong Min Choi and Sang Chul Chong in Psychological Science

Footnotes

Acknowledgements

All data were presented at the 2019 Vision Sciences Society meeting.

Transparency

Action Editor: Philippe G. Schyns

Editor: D. Stephen Lindsay

Author Contributions

Y. M. Choi and S. C. Chong jointly developed the study concept and design. Y. M. Choi conducted testing and data collection under the supervision of S. C. Chong. Both authors analyzed and interpreted the data. Y. M. Choi drafted the manuscript, and S. C. Chong provided critical revisions throughout the process. Both authors approved the final manuscript for submission.

ORCID iD

Sang Chul Chong

References

Allik

Toom

Raidvee

Averin

Kreegipuu

(2013). An almost general theory of mean size perception. Vision Research, 83, 25–39. doi:10.1016/j.visres.2013.02.018

Alvarez

G. A.

(2011). Representing multiple objects as an ensemble enhances visual cognition. Trends in Cognitive Sciences, 15, 122–131. doi:10.1016/j.tics.2011.01.003

Anderson

S. F.

Kelley

Maxwell

S. E.

(2017). Sample-size planning for more accurate statistical power: A method adjusting sample effect sizes for publication bias and uncertainty. Psychological Science, 28, 1547–1562. doi:10.1177/095679761772372

Anton-Erxleben

Carrasco

(2013). Attentional enhancement of spatial resolution: Linking behavioural and neurophysiological evidence. Nature Reviews Neuroscience, 14, 188–200. doi:10.1038/nrn3443

Baek

Chong

S. C.

(2020). Distributed attention model of perceptual averaging. Attention, Perception, & Psychophysics, 82, 63–79. doi:10.3758/s13414-019-01827-z

Benjamin

D. J.

Berger

J. O.

Johannesson

Nosek

B. A.

Wagenmakers

E.-J.

Berk

. . . Johnson

V. E.

(2018). Redefine statistical significance. Nature Human Behaviour, 2, 6–10. doi:10.1038/s41562-017-0189-z

Brady

T. F.

Alvarez

G. A.

(2011). Hierarchical encoding in visual working memory: Ensemble statistics bias memory for individual items. Psychological Science, 22, 384–392. doi:10.1177/0956797610397956

Brainard

(1997). The Psychophysics Toolbox. Spatial Vision, 10, 433–436. doi:10.1163/156856897X00357

Carrasco

(2011). Visual attention: The past 25 years. Vision Research, 51, 1484–1525. doi:10.1016/j.visres.2011.04.012

10.

Carrasco

Barbot

(2019). Spatial attention alters appearance. Current Opinion in Psychology, 29, 56–64. doi:10.1016/j.copsyc.2018.10.010

11.

Cha

Chong

S. C.

(2018). Perceived average orientation reflects effective gist of the surface. Psychological Science, 29, 319–327. doi:10.1177/095679761773553

12.

Chong

S. C.

Joo

S. J.

Emmanouil

T. A.

Treisman

(2008). Statistical processing: Not so implausible after all. Perception & Psychophysics, 70, 1327–1334. doi:10.3758/PP.70.7.1327

13.

Chong

S. C.

Treisman

(2003). Representation of statistical properties. Vision Research, 43, 393–404. doi:10.1016/S0042-6989(02)00596-5

14.

Chong

S. C.

Treisman

(2005). Attentional spread in the statistical processing of visual displays. Perception & Psychophysics, 67, 1–13. doi:10.3758/BF03195009

15.

De Fockert

J. W.

Marchant

A. P.

(2008). Attention modulates set representation by statistical properties. Perception & Psychophysics, 70, 789–794. doi:10.3758/PP.70.5.789

16.

Gobell

Carrasco

(2005). Attention alters the appearance of spatial frequency and gap size. Psychological Science, 16, 644–651. doi:10.1111/j.1467-9280.2005.01588.x

17.

Haberman

Whitney

(2007). Rapid extraction of mean emotion and gender from sets of faces. Current Biology, 17, R751–R753. doi:10.1016/j.cub.2007.06.039

18.

Hubert-Wallander

Boynton

G. M.

(2015). Not all summary statistics are made equal: Evidence from extracting summaries across time. Journal of Vision, 15(4), Article 5. doi:10.1167/15.4.5

19.

H. Y.

Chong

S. C.

(2009). Computation of mean size is based on perceived size. Attention, Perception, & Psychophysics, 71, 375–384. doi:10.3758/APP.71.2.375

20.

H. Y.

Park

W. J.

Chong

S. C.

(2015). Ensemble statistics as units of selection. Journal of Cognitive Psychology, 27, 114–127. doi:10.1080/20445911.2014.985301

21.

JASP Team. (2017). JASP (Version 0.10) [Computer software]. Retrieved from https://jasp-stats.org/

22.

Jeffreys

(1961). The theory of probability (3rd ed.). Oxford, England: Oxford University Press.

23.

Kanaya

Hayashi

M. J.

Whitney

(2018). Exaggerated groups: Amplification in ensemble coding of temporal and spatial features. Proceedings of the Royal Society B: Biological Sciences, 285(1879), Article 20172770. doi:10.1098/rspb.2017.2770

24.

Kirsch

Heitling

Kunde

(2018). Changes in the size of attentional focus modulate the apparent object’s size. Vision Research, 153, 82–90. doi:10.1016/j.visres.2018.10.004

25.

Kleiner

Brainard

D. H.

Pelli

D. G.

(2007). What’s new in Psychtoolbox-3? Perception, 36(ECVP Abstract Suppl.).

26.

Lee

Baek

Chong

S. C.

(2016). Perceived magnitude of visual displays: Area, numerosity, and mean size. Journal of Vision, 16(3), Article 12. doi:10.1167/16.3.12

27.

K. A.

Yeh

S. L.

(2017). Mean size estimation yields left-side bias: Role of attention on perceptual averaging. Attention, Perception, & Psychophysics, 79, 2538–2551. doi:10.3758/s13414-017-1409-3

28.

Z. L.

Dosher

B. A.

(1998). External noise distinguishes attention mechanisms. Vision Research, 38, 1183–1198. doi:10.1016/S0042-6989(97)00273-3

29.

Myczek

Simons

D. J.

(2008). Better than average: Alternatives to statistical summary representations for rapid judgments of average size. Perception & Psychophysics, 70, 772–788. doi:10.3758/PP.70.5.772

30.

Palmer

(1990). Attentional limits on the perception and memory of visual information. Journal of Experimental Psychology: Human Perception and Performance, 16, 332–350. doi:10.1037/0096-1523.16.2.332

31.

Parkes

Lund

Angelucci

Solomon

J. A.

Morgan

(2001). Compulsory averaging of crowded orientation signals in human vision. Nature Neuroscience, 4, 739–744. doi:10.1038/89532

32.

Pelli

(1997). The VideoToolbox software for visual psychophysics: Transforming numbers into movies. Spatial Vision, 10, 437–442. doi:10.1163/156856897X00366

33.

Persuh

Genzer

Melara

(2012). Iconic memory requires attention. Frontiers in Human Neuroscience, 6, Article 126. doi:10.3389/fnhum.2012.00126

34.

Proulx

M. J.

(2010). Size matters: Large objects capture attention in visual search. PLOS ONE, 5(12), Article e15293. doi:10.1371/journal.pone.0015293

35.

Rodriguez-Cintron

L. M.

Wright

C. E.

Chubb

Sperling

(2019). How can observers use perceived size? Centroid versus mean-size judgments. Journal of Vision, 19(3), Article 3. doi:10.1167/19.3.3

36.

Son

B.-I.

Kang

M.-S.

Chong

S. C.

(2020). Similarity-based clusters are representational units of visual working memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 46, 46–59. doi:10.1037/xlm0000722

37.

Souza

A. S.

Oberauer

(2016). In search of the focus of attention in working memory: 13 years of the retro-cue effect. Attention, Perception, & Psychophysics, 78, 1839–1860. doi:10.3758/s13414-016-1108-5

38.

Sweeny

T. D.

Haroz

Whitney

(2013). Perceiving group behavior: Sensitive ensemble coding mechanisms for biological motion of human crowds. Journal of Experimental Psychology: Human Perception and Performance, 39, 329–337. doi:10.1037/a0028712

39.

Teghtsoonian

(1965). The judgment of size. The American Journal of Psychology, 78, 392–402. doi:10.2307/1420573

40.

Wagenmakers

E.-J.

Marsman

Jamil

Verhagen

Love

. . . Morey

R. D.

(2018). Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications. Psychonomic Bulletin & Review, 25, 35–57. doi:10.3758/s13423-017-1343-3

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.61 MB